Using group theory to understand B meson decays

The up, down, and strange quarks can be thought of as elements of an SU(3) group due to the similarity in their masses. We utilize this fact to investigate the properties of the bottom quark in charmless B meson decays. Our focus is on final states consisting of three pseudoscalar mesons. Using SU(3) representations for the quarks, we demonstrate how to construct the three-body final states. We show that there are 120 fully-symmetric and 56 fully-antisymmetric final states under the interchange of any two final-state mesons. We calculate the three-body decay amplitude in terms of parameters of the Standard Model (SM). We present relations between SU(3) matrix elements and establish a way to determine a key parameter in the SM, the weak phase γ. Our work seeks to create new methods for measuring γ, thereby improving its precision and accuracy.